To find the angle measures using the expression you've provided, \( (7x - 9) + 4x \), you'll first need to simplify the expression:
- Combine like terms: \[ 7x + 4x - 9 = 11x - 9 \]
Now you have the simplified expression \( 11x - 9 \).
To determine specific angle measures, you would typically set this expression equal to a known angle or some condition. For example, if you need to determine the angle measures equal to a straight angle (180 degrees), the equation would look like this:
\[ 11x - 9 = 180 \]
You would then solve for \( x \):
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Add 9 to both sides: \[ 11x = 180 + 9 \] \[ 11x = 189 \]
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Divide both sides by 11: \[ x = \frac{189}{11} \] \[ x \approx 17.18 \]
Then you would substitute \( x \) back into the angle measure \( (7x - 9) \) or \( (11x - 9) \) to find the angle:
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Calculate \( (7x - 9) \): \[ 7 \left(\frac{189}{11}\right) - 9 = \frac{1323}{11} - \frac{99}{11} = \frac{1224}{11} \approx 111.27 \]
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Calculate \( (11x - 9) \) for another angle measure: \[ 11 \left(\frac{189}{11}\right) - 9 = 189 - 9 = 180 \]
In summary, to determine exact angle measures, you typically need an equation or context, like setting equal to 180 degrees for a straight angle or using specific relationships between angles (if applicable).